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AM, FM, and Digital Modulated Systems Chap. 5
where K depends on the gain of the receiver and the loss in the channel. In detecting SSB
signals with audio modulation, the reference phase u 0 does not have to be zero, because the
same intelligence is heard regardless of the value of the phase used [although the v out (t) waveform
will be drastically different, depending on the value of u 0 ]. For digital modulation, the
phase has to be exactly correct so that the digital waveshape is preserved. Furthermore, SSB
is a poor modulation technique to use if the modulating data signal consists of a line code with
a rectangular pulse shape. The rectangular shape (zero rise time) causes the value of the SSB-
AM waveform to be infinite adjacent to the switching times of the data because of the Hilbert
transform operation. (This result will be demonstrated in a homework problem.) Thus, an
SSB signal with this type of modulation cannot be generated by any practical device, since a
device can produce only finite peak value signals. However, if rolled-off pulse shapes are used
in the line code, such as (sin x)x pulses, the SSB signal will have a reasonable peak value,
and digital data transmission can then be accommodated via SSB.
SSB has many advantages, such as a superior detected signal-to-noise ratio compared to
that of AM (see Chapter 7) and the fact that SSB has one-half the bandwidth of AM or DSB-SC
signals. (For additional information on this topic, the reader is referred to a book that is devoted
wholly to SSB [Sabin and Schoenike, 1987].)
Vestigial Sideband
In certain applications (such as television broadcasting), a DSB modulation technique takes too
much bandwidth for the (television) channel, and an SSB technique is too expensive to implement,
although it takes only half the bandwidth. In this case, a compromise between DSB and
SSB, called vestigial sideband (VSB), is often chosen. VSB is obtained by partial suppression of
one of the sidebands of a DSB signal. The DSB signal may be either an AM signal (that is, it has
a discrete carrier term) or a DSB-SC signal. This approach is illustrated in Fig. 5–6, where one
sideband of the DSB signal is attenuated by using a bandpass filter, called a vestigial sideband
filter, that has an asymmetrical frequency response about ; f c . The VSB signal is given by
s VSB (t) = s(t) * h v (t)
(5–30)
where s(t) is a DSB signal described by either Eq. (5–4) with carrier or Eq. (5–13) with suppressed
carrier and h v (t) is the impulse response of the VSB filter. The spectrum of the VSB
signal is
S VSB (f) = S(f)H v (f)
(5–31)
as illustrated in Fig. 5–6d.
The modulation on the VSB signal can be recovered by a receiver that uses product
detection or, if a large carrier is present, by the use of envelope detection. For recovery of
undistorted modulation, the transfer function for the VSB filter must satisfy the constraint
H v (f - f c ) + H v (f + f c ) = C, |f| … B
(5–32)
where C is a constant and B is the bandwidth of the modulation. An application of this
constraint is shown in Fig. 5–6e, where it is seen that the condition specified by Eq. (5–32) is
satisfied for the VSB filter characteristic shown in Fig. 5–6c.